Saving rendered image into a file doesn't work
You have to actually render your image first before you can save your render as a file. To do that press F12 while your cursor is over your 3D View window.

Wait for the render to finish and only after that with the mouse cursor hovering the rendered image can you press F3 to save it. Alternatively if the hotkey for some reason is not working you can save your render by going to the Image Menu > Save Image As, by default at the bottom of the UV Image  Window

Are you using a laptop computer by any chance? Some computers by default use the function keys F1  to F12 as direct shortcut keys for Microsoft Office or other Microsoft applications, and to use them as regular F keys you have to press the Fn button on your keyboard.